Estimation of domain truncation error for a system of PDEs arising in option pricing

ArXiv ID: 2401.15570 “View on arXiv”

Authors: Unknown

Abstract

In this paper, a multidimensional system of parabolic partial differential equations arising in European option pricing under a regime-switching market model is studied in details. For solving that numerically, one must truncate the domain and impose an artificial boundary data. By deriving an estimate of the domain truncation error at all the points in the truncated domain, we extend some results in the literature those deal with option pricing equation under constant regime case only. We differ from the existing approach to obtain the error estimate that is sharper in certain region of the domain. Hence, the minimum of proposed and existing gives a strictly sharper estimate. A comprehensive comparison with the existing literature is carried out by considering some numerical examples. Those examples confirm that the improvement in the error estimates is significant.

Keywords: option pricing, partial differential equations (PDE), regime-switching models, domain truncation error, finite difference methods, Options

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly theoretical, focusing on the derivation of sharp error bounds for a complex system of parabolic PDEs using advanced analysis (semigroup theory, stochastic processes, and rigorous estimates), which places it in the high math complexity range; however, it is light on empirical implementation details, offering only numerical examples for verification without code or backtesting, indicating low empirical rigor.
  flowchart TD
    A["Research Goal<br>Estimate domain truncation error<br>for PDEs in regime-switching option pricing"] --> B["Data & Inputs<br>European options under<br>regime-switching market model"]
    B --> C["Methodology<br>Derive theoretical error estimates<br>for truncated domain"]
    C --> D{"Computational Process<br>Numerical approximation<br>using finite difference methods"}
    D --> E["Key Findings<br>Sharper error estimates<br>than existing literature"]
    E --> F["Validation<br>Numerical examples confirming<br>significant improvement"]